Question

Unique foods operates three plants in the world. Summary data for each is shown below
Plant
UK USA Canada
Total Fixed Cost(TFC) 1,00,000 2,00,000 4,00,000
Variable Cost Per Unit (AVC) 10 8 5
Output price per unit (P) 20 22 18
Capital / Labor Ratio (K/L) 2:1 3:1 4:1
Output rate (Q) 22,000 16,000 33,000
Determine the profit elasticity for each plant

Answer 1

Answer on Question # 74285, Economics / Microeconomics

Question: Unique foods operates three plants in the world. Summary data for each is shown below

Plant

UK USA Canada

Total Fixed Cost(TFC) 100,000 200,000 400,000

Variable Cost Per Unit (AVC) 10 8 5

Output price per unit (P) 20 22 18

Capital / Labor Ratio (K/L) 2:1 3:1 4:1

Output rate (Q) 22,000 16,000 33,000

Determine the profit elasticity for each plant

Answer:

$$\text{profit elasticity} = \frac{(Q_2 - Q_1)}{Q_1} \cdot \frac{((P_{r_2} - P_{r_1}) / P_{r_1})}{\text{1)}}$$

1) For UK:

$$\begin{array}{l} TC = 100,000 + (10 \times 22,000) = 320,000 \\ TR = 22,000 \times 20 = 440,000 \\ P_{r_1} = 440,000 - 320,000 = 120,000, \text{ when } Q_1 = 22,000 \\ \text{But when } Q_2 = 24,000, TC = 100,000 + (10 \times 24,000) = 340,000 \\ TR = 24,000 \times 20 = 480,000 \\ P_{r_2} = 480,000 - 340,000 = 140,000 \\ \end{array}$$

Then profit elasticity = $\frac{(24,000 - 22,000)}{22,000} \cdot \frac{((140,000 - 120,000) / 120,000)}{0.55} = 0.55$

2) For Usa:

$$\begin{array}{l} TC = 200,000 + (8 \times 16,000) = 328,000 \\ TR = 16,000 \times 22 = 352,000 \\ P_{r_1} = 352,000 - 328,000 = 24,000, \text{ when } Q_1 = 16,000 \\ \text{But when } Q_2 = 18,000, TC = 200,000 + (8 \times 18,000) = 344,000 \\ TR = 18,000 \times 22 = 396,000 \\ \end{array}$$ $$\Pr_{2} = 396,000 - 344,000 = 52,000$$ $$\text{Then profit elasticity} = \frac{(18,000 - 16,000)}{16,000} / \frac{(52,000 - 24,000)}{24,000} = 0.11$$

3) For Canada:

$$\begin{array}{l} TC = 400,000 + (5 \times 33,000) = 565,000 \\ TR = 33,000 \times 18 = 594,000 \\ Pr_{1} = 594,000 - 565,000 = 29,000, \text{ when } Q_{1} = 33,000 \\ \text{But when } Q_{2} = 35,000, TC = 100,000 + (5 \times 35,000) = 575,000 \\ TR = 35,000 \times 18 = 630,000 \\ Pr_{2} = 630,000 - 575,000 = 45,000 \\ \end{array}$$ $$\text{Then profit elasticity} = \frac{(35,000 - 33,000)}{33,000} / \frac{(45,000 - 29,000)}{29,000} = 0.11$$

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